In this paper, the authors propose an integer linear programming (ILP) model for static multi-car elevator operation problems. Here, “static” means that all information which make the behavior of the elevator system indeterministic is known before scheduling. The proposed model is based on the trip-based ILP model for static single-car elevator operation problems. A trip of an elevator is a one-directional movement of that elevator, which is labaled upward or downward. In the trip-based ILP model, an elevator trajectory is scheduled according to decision variables which determine allocations of trips to users of an elevator system. That model has such an advantage that the difficulty in solving ILP formulations resulted by that model does not depend on the length of the planning horizon nor the height of the considered building, thus is effective when elevator trajectories are simple. Moreover, that model has many variables relevant to elevators' positions. The proposed model is resulted by adding 3 constraints which are basically based on those variables and make it possible to prevent elevators in a same shaft from interfering. The first constraint simply imposes the first and last floors of an upper trip to be above those of its lower trip. The second constraint imagines the crossing point between upper and lower trips and imposes it ahead of or behind the lower trip according to their directions. The last constraint estimates future positions of elevators and imposes the upper trip to be above floors of passengers on the lower trip. The basic validity of the proposed model is displayed by solving 90 problem instances and examining elevator trajectories generated from them, then comparing objective function values of elevator trajectories on a multi-car elevator system with those on single-car elevator systems.

In this paper, we aim to develop technologies for the circuit fault diagnosis and propose a formulation of a measure of a test pattern for the circuit fault diagnosis. Given a faulty circuit, the fault diagnosis is to deduce locations of faults that had occurred in the circuit. The fault diagnosis is executed in software before the failure analysis by which engineers inspect physical defects, and helps to improve the manufacturing process which yielded faulty circuits. The heart of the fault diagnosis is to distinguish between candidate faults by using test patterns, which are applied to the circuit-under-diagnosis (CUD), and thus test patterns that can distinguish as many faults as possible need to be generated. This fact motivates us to consider the test pattern measure based on the number of fault-pairs that become distinguished by a test pattern. To the best of the authors' knowledge, that measure requires the computational time of complexity order O(NF2), where NF denotes the number of candidate faults. Since NF is generally large for real industrial circuits, the computational time of the measure is long even when a high-performance computer is used. The formulation proposed in this paper makes it possible to calculate the measure in the computational complexity of O(NF log NF), and thus that measure is useful for the test pattern selection in the fault diagnosis. In computational experiments, the effectiveness of the formulation is demonstrated as samples of computational times of the measure calculated by the traditional and the proposed formulae and thorough comparisons between several greedy heuristics which are based on the measure.